A bicycle with 0.80m diameter tires is coasting on a level road at 5.6m/s. a small blue dot has been painted on the tread of the rear. What is the angular speed of the tires

The circumference of the tire is (0.8 π) meters.

The rate at which the tires rotate is (5.6 m/s) / (0.8 π m) = 7 / π rev per sec

Each rev is 2π radians. So the angular speed of the rotating tire is

(7 / π) x (2π) = 14 radians per sec.

The speed would have been the same even if there were no small blue dot

on the tread, or if the dot were painted in some other color.